The Cross Product

[DBZM1k3]

Never mind, after checking the maths I've found out that it does matter which order you cross the vectors. Thanks for the great tutorial. =D

[DBZM1k3]

Just curious, if you do vector b and you cross it with vector a in that order do you get the opposite of the example you got in the video? The only reason I ask this is I was doing a tutorial for one of my lectures and in that lecture we had to make a cube in 3d space. While doing this I entered my Vectors in an anti-clockwise format which put the normal on the wrong side of the face. Entering them in a clockwise format fixed this, so is it because of the way the vectors were crossed or not?

[limkerfins]

thank ya broseph brosephsons

[29varrie]

Hello Patrick!

I am an avid fan of your very down to earth vids. But do you have videos regarding vectors in three dimensions? like regarding parametric/symmetric equations, quadric surfaces...etc.

Thanks!

[jorgeg922]

nice vid, way better than my physics prof

[ViketheTrue]

do you have a video where you are given i and j and are asked to find the vector product

[11m0]

You've inspired me to make my own math videos. But how do you position the camera to get a shoot that focuses solely on the paper?

[quysauce12]

i love you patrick.

[mrwmarine]

Holy crap. Thank you so much. Keep these videos coming, they are helping me tremendously. I may be requesting topics for you to cover if I'm having any more trouble in the future.

[IamMetal92]

Soooooo much simpler than my idiot teacher's video! Thank you!

[cglg1234]

i'm gonna learn this at school this week, this video helped prepare me for whats to come thanks :)

[wickedbardrenthead]

We had a snow day today and everyone got to go home early, but I missed the notes over Cross Product for my Pre-Cal assignment. Thank you SOOOO much. You literally just taught math 200 times better than my teacher! Thank you and God bless! :)

[Deeharok]

5:12, 1 * -1 = +1? o:

[leidem]

@Deeharok "Minus one times negative one", ie. - ( 1 * -1) = 1

[hueyp98]

In my book, it has all positive i.e. a1 + a2 +a3, while you have '-' a2 times the 2X2 matrix. Would you mind explaining that to me. Thanks.

[freakmanification]

learnt more watching this 8 min video than sitting in class for 1 hour... thank you.

[Targ1tay]

thank you so much! It's all clear to me now

[TheDamped]

Thanks for this! Very easy to understand compared to the other information I have ran across, considering I remember very little of mathematical notations.

[martinberger84]

Very to the point! It helped. Thanks for this video.

[ilovegemgem]

thank u

[ArcticGooner]

my teacher took 2 hours explaining this you took 10 minutes call it AMAZING

[travelleraroundworld]

Cross product and dot product combo question. Given |a|=2, |b|=3 (mangnitudes of vectors a,b), find: (axb)(axb) + (a.b)(a.b). For the dot product part (a.b)(a.b), I figure it's: (a.b)^2= a^2+2ab+b^2， which yields 16 (a^2, b^2 should not change magnitude as a.a=a, I am not quite sure what to do with 2ab - I just multiplied the magnitudes). Towards the part of cross product I am confused. Any help, please? Thank you for your videos, I am a fan by now.

[ilovetayer]

do you have a video on vector triple products?

[patrickJMT]

@ilovetayer nope, sorry!

[damudread]

Thank you sir! And God bless you!

[brad5191]

hey PatrickJMT.. thanks for getting me through college calculus.

[patrickJMT]

@brad5191 glad i could help you : )

[hajlan91]

omg your a life saver :D

[19WL88]

can you post more video involving theories instead of solving particular problems?

[way2fasts]

i wish you were my math teacher

[Blacksnowman]

why do we minus the J component?

[AmateurDrumCovers]

Got a C+ in calculus I, started watching your videos for calculus II last year, and got an A. Thanks!

[loik345]

How to cross product of two vectors which are 2D.

[patrickJMT]

@loik345 you dont. the cross product is defined for vectors in 3d

[loik345]

@patrickJMT Thanks for the info.

[TookMe20min2findThis]

@patrickJMT

Well, perhaps he meant a cross product of 2 vectors that don't have a third dimension (that is they each lie on a 2D plane). Obviously the Cross product will create a 3rd dimension but the operation is of course valid.

[Kinggenton]

one question my calculus three teacher says that for the j component you have to substract it the other way and i say you but a negative on the outside!!!

this confuses me a little cuz in side a2 you switched it from positive to negative and outside had a negative side

so no i am asking........ in i,j,k j must always be negative?

and do you always have to minus the minus to get a positive in j?



[YoungThaddeus]

Thank you soo much. After 4 years of using youtube I finally decided to make an account just so i could subscribe to you.

[patrickJMT]

@YoungThaddeus ha ; ) 

[smhouse07]

It would be awesome if you created an application for smart phones, most students are always on the go, watching ur videos during anytime we can is very useful: just a good idea I thought I could share with you

[patrickJMT]

@smhouse07 there are some calculus apps on itunes

[lilonotstitch]

your way of teaching is sooooooooooooooooooooooo good! i love math now! welll in this video it's physics :D but MATH AND PHYSICS FTW

[kabilan83]

ur the best ever bro

[GohansRiceBall]

Is there a video about the dot product and cross product identities?

[lobsidedballs]

i <3 u man

[cuteNOBITA]

thanX a lot patrickJMT........ i LOVE ur video very much..... ur video help me a lot......

[cr656565]

patrickJMT + kahnacademy = my life saved

[cuteNOBITA]

@cr656565 me too...... thanX Mr.patrickJMT ^^

[aditya95sriramgmail]

In the example at 0:59 if it would have been b x a, would the cross product have been pointing the other direction as per the right hand rule

[DodgeMuscle89]

@aditya95sriramgmail yea im pretty sure it would be, thats why its important to get the right order of axb

[soverign87]

man thank you a lot that's helped me a big time :)

[THEBLACK493]

I AM CONFUSED AT 3:58

[MurdockIX]

@THEBLACK493

That's the determinant of a 3x3 matrix.

[owdi2631992]

what if you have three points, a, b and c, would you do the same thing as well?

[zhengyucui]

lol you're married...couldn't help but notice

[gorfendall]

Finding this made Calc 3 and Physics so much easier! Thank you so much for your neat handwriting, magic whiteboard, clear voice and awesome teaching skills. Thanks @patrickJMT !!

[AryaSravaka]

I have Calculus 3 exam at university of london with in a month & also number theory.. Cal3 notes i got are a huge mess.. thanks for your all the work. i will be watching most of your videos. Be well, with metta

[AryaSravaka]

thanks a lot sir

[BlackTheDen]

HEy @patrickJMT nice video, extremely helpful. Hey is it possible if you could illustrate how to do word problems on vectors.

Thanks

[lilpeacey]

Thank you for being good at explaining and taking the time to make these videos. I've been trying to learn vectors all quarter from a professor who moves too fast and isn't very clear, and this helped me finally get it. Thanks!

[Nagato180]

is there a big difference between martix notation and coordinate notation?

[KaZ5849]

Woo i can do it, ty for this, exam in the morning :D

[MrsxGracex]

thanks for this!:)

[TwrZ]

your handwriting is very pleasant to look at and thanks, this was very helpful

[s87343jim]

So I'm just wondering, if AXB, is it the same thing as (|A||B|) (sin ● )(n)?

I just want to know is there any difference between the Patrick's menthod, and the one I got thought else where.

Where ● is just an angle, and n is an unit vector. 

[hashmat187]

are you a youtube partner?

[hashmat187]

wow. the first 3d visual example i've ever had in a math lesson. 5 stars!

[tadm123]

How you get the cross product of a 4x4 or 5x5 , etc ?

[MikelSeo]

@tadm123 the cross product is only defined for the 3rd dimension. it doesn't apply to 4x4 or 5x5.

[lucpilon1]

Awesome video very helpful, and not hard to understand thx man

[brad5191]

Can you do an example with three vectors, such as (3,1,0) x (2,4,0) ?

[iluvelectrik]

@brad5191 That's two vectors lol It just has three components. It works exactly the same way as in the video.

[brad5191]

@iluvelectrik yeah solid, thanks

[TheSideduck]

People complain about ads, but I want you to know that what you do is beyond amazing, and I'd sit through way more ads if it would help you do what you do. You deserve to be able to get something from your work.

[aishaprasad]

Thank you so much for your videos!! They are really helpful. I used them for studying for AP Calculus BC and IB Math HL! Please let your videos stay free, because I know I'll need them for college! :)

[iancurtis123]

you da man

[knahero010]

Great video! Is there one that talks about parallelepipeds?

[toiletooth]

Thank you so much. This was exactly what I needed.

[chicogotgreen]

Not exactly sure why we pay for the first two years of college these days... Your video are clearer and more concise than any lecture I have ever had... and thats at $30K+ a year tuition. Sad.

Awesome videos. Very helpful in quite a few areas.

[bodinian]

but can you do the cross product of 3 vectors?

[patrickJMT]

@bodinian what would that mean?

[bodinian]

@patrickJMT I have no idea

[titan59]

@patrickJMT Prove that the vector is orthogonal to three vectors?. . . but i guess you only need it to be orthogonal to two, in order to be ortho. to all three, huh?

[phelepone]

@patrickJMT 4D :D

[bobiffer0123]

@bodinian cross product two of them then use the answer to that one and cros product with the third

[20thCenturyG4M1NG]

@bodinian Yes but it would take much longer, you find the cross product of two of them then use that vector with the 3rd for the final cross product

[helibbc]

Now I study at "patrickJMT" University! =D

[patrickJMT]

@helibbc tuition is free! just sit through an ad now and again : )

[brad5191]

@patrickJMT Wow, you know what? If the whole world realized that it doesn't take big money to become smarter than your professors, I think we would be in a better state of mind as a country.

[AirspaceFalling]

@patrickJMT ...Or use adblock for firefox and see no ads at all :P

[helibbc]

@helibbc You helped me in cross and dot product. Also, All the types of series. Thanks a lot I did really good in the calculus and statics midterms =D

[vidyadbz]

@helibbc Hahahahahahhahah LOL =_="

[archerjeffry]

hoo its some what worth thanks for u alot

actually im very weak in this concept but u made it clear within 10 minutes which my proffesor ccant in 1 hr

thanks alot

[ClownDatWalk]

what do i do without u lol

[smilerLFC]

Just don't get the - negative values. -1 x 1 = -1... i can't see where the other negatives are appearing from to make it a plus :(.

[smilerLFC]

@smilerLFC Think i get it!!! When performing the multiplication Each (?-?) has a minus sign already in there. As you aim to take one vector away from the other. Works for me anyway.

[b2g4]

how do u find the are of the triangle with a and b as two of its sides after you find the cross product?

[TheBjmccullough]

Patrick,

What if one of the products is missing ? Say for instance, I have ijk values for vector a, but only ik for vector b. Does that imply j exists as 1 ?

[jmazz17]

@TheBjmccullough j will be zero i believe

[santiagodiaz06]

@TheBjmccullough

it means that value for j is 0

[arielleviolin]

This is so helpful; thank you!

[OhEmGeeItsReptar]

Should have watched this 2 weeks ago!!!! I have a Statics exam tomorrow and you just [maybe have] saved my ass.

[melodiaagrodolce]

Hi, Im sorry but I didn't understand one thing in the video. When you are solving for the j cross product I understand why you get 10 but why does the 4 become positive? 5 cross 2 is 10 but 4 cross -1 was 4. Does it have to do with the minus sign out front? And if that is the case why did the 10 stay positive?

Thanks a tonne if anyone can answer my question!

[Nikon05]

hey patrick! For the first formula you gave for 2 vectors @ 0:20, is the middle value not supposed to be "a1b3 - a3b1"?

[kitten0001x]

thanks.. :) i wish you also have triple product..

[oppasiun]

sexy hand hahahahaha 

[Gilster85]

Great tutorial but....... the ad before the video is annoying!

[Gilster85]

Great tutorial but....... the ad before the video is very annoying!

[Gilster85]

Great tutorial but....... hate the ad before the video! Please remove it. Its ruining it.

[o0Vox]

Good video on how to do it. Can anyone show me a video on why it is done that way?

[LAnonHubbard]

Good video.

[beastlt12]

Thanks for the video. A short, sweet, and to the point refresher.

[JayZeus7]

Love your videos!

Just a suggestion:

You should consider making a video about scalar triple products~

[birdsofafeather1990]

This is so much easier than my lecture notes - this professor used loads of really pompous and complicated notation. This is crystal clear!

[kabayanhustler]

Thanks a lot man!

[DeLilleD]

I prefer this right-hand rule:

If you hold the thumb, index finger and middle finger of your right hand like the vectors (2 vectors in a plane and the other vector perpendicular), then point your thumb in the direction of a and your index finger in the direction of b, your middle finger will point towards the cross product.

It's as easy as (counting) 1, 2, 3 (on your fingers).

[blumpkin123456789]

Right now i just started the new quarter of engineering classes and i forgot all my vector calculus and differential equations and if it wasnt for you i would be completely done for... Thank You

[Jiggajigg81]

I never took Calc 3, wish you indicated some way what video/topic to focus on next. I still give all your videos thumbs tho

[Hell01234u]

Yeah great job on the tutorial, Thanks a lot!

[crillium]

Thank you so much!

[harj2009]

I love u for real

[shortie989]

Thanks so much, very clear and easy to understand :)

[patrickJMT]

@shortie989 glad u liked it!

[Daneish09]

thanks for the vids :) i learned a lot!

[uburhan]

Nice video, thanks :)

[olgakayy]

I didnt understand a word u just said. sorry!

[patrickJMT]

@olgakayy i forgive you if you can not understand.

[MrHirdepal]

ur videos on vectors helped me a lot in physics...thanks..keep uploading more..

[tvdang7]

thanks. i will click all your ads so you get paid.

[sundancekid122]

Fuck becoming a professor, Public School/University will be dead in 20 Years when everyone can get everything they need off the internet.

[patrickJMT]

@sundancekid122 ha, never.

[IShallEatYou]

@patrickJMT yeah i agree. Businesses will never quit making you have that piece of paper.

[Deltad]

@sundancekid122 it's people like you that give us Math teacher jobs. and what good are these info off the internet if you're too stupid to use it. hmmmm?

[UsedDoor]

@sundancekid122 That's true. But what's scary is that people will have answers, without knowing how to find it. In 20 years, people will google 10+1=11, without knowing how to do it on paper. "10+1? I don't know, let's look it up!"

[mrpaper201010]

why do we have negative sign(-) for J? Thanks

[paulchae8]

a1 a2 a3 a1 a2 a3 | \/ \/ \/ |

b1 b2 b3 b1 b2 b3

easier way of doing it, so just plug in the values of the vector a and b as indicated

then skip the the 4 values (first and last of each line as indicated by |)

then multiply the a2b3 (as indicated by the \) and multiply a3 b2 (as indicated by the /)

then do that with all of the values as shown in the diagram ( \, /)

then you should get (a2b3 +- a3b2, a3b1 +-a1b3, a1b2+-a2b1) (it is plus or minus depending on the values)

=answer:)

[paulchae8]

@paulchae8 it is kinda hard to show typing

if any questions pm and i will answer your questions and post a vid if necessary

[mrpaper201010]

Your lessons are awesome Pat! do you have any videos about augmented matrices?

[mrpaper201010]

your one of a kind!

[yondaime500]

Your videos are a very efficient way of learning. You explain things really well without taking too long. By the way, this 3x3 matrix method is how I learned in Physics class, but my Analytic Geometry teacher said that it's not mathematically correct, because i,j and k are vectors and you can't put vectors on a matrix. So some math teachers might not accept it as a valid answer on a test, and it's better to skip the 3x3 matrix and just do the cofactors.

[frankbridenhagen]

Great explanation!!!!

[harisGTJ]

patrick,thnank you very much, just had my 1st lecture about graphics in computer science and we got told to use the cross product, but didnt get told how, thank you very much, btw ive watched ur how to multiply a matrix video loads of times because i still get it wrong alot, i might be at university, but im still relying on youtube, thnks man

[sloppyjoes7]

Patrick,

Your videos are better than KhanAcademy's, except he has more videos than you.

The big difference?

You don't make mistakes. I don't know how you do it, but you don't. Khan makes mistakes all the time, and it's distracting.

However, his intro to Diff Eq is better, because.... you don't have one.

[patrickJMT]

@sloppyjoes7 glad you like my vids although there are plenty with mistakes so i have them too. there are about a million videos i want to make, diff eq is part of them, however my day job prevents me from just sitting around and making them.

[abaddon1112]

@sloppyjoes7 no one is perfect, and Khan is doing good by providing a lot of knowledge to people for free. The only one that never makes mistakes is God.

[patrickJMT]

@abaddon1112 yes, there is plenty of room on the internet for all!

[hooknshlimer]

Have you ever thought of becoming a professor, except a good one that can actually explain things

[patrickJMT]

@hooknshlimer the original plan was to get a phd and be a professor, but those plans are now gone!

[echoray2736]

*bows down*

[pureXsolitude]

thank you!!! i have an exam tomorrow this helped me alot!

[StephMGII]

Thanks for the video, it helped!

[shinomora]

thank you patrickJMT you rock!

[viper56610]

Thanks so much Patrick! Sadly, I learn more from your videos than I do in my professor's lectures. Keep doing what you're doing!

[mcpimpen]

my teacher did such a horrible job explaing this... thx!

[Cyphlix]

Every video you make is part of a proof that you sir, are a GOD :)

[patrickJMT]

@Cyphlix thanks, but i am just a typical person, like most everyone else

[Chimpalimp1001]

Could you by chance tell me what is the use of vector projections? ( I haven't been able to find any source that really tells me any use for them except because I was told to use them in a homework problem.)

[svalmazan]

this refers to the formula for the cross product of vectors with three components.  please tell me why the second term is negative. thanks a lot.

[ammatzner]

Thanks to you I got a B in Cal II :). I made it through by reading the book and taking notes from it while I was in class, watching your videos, and ignoring my hopelessly confusing instructor. Looks like you'll be carrying me through Cal III as well. Thank you so much for your help.

[patrickJMT]

@ammatzner ha, no problem : )

[hasben0]

@patrickJMT This guy and i are on the same boat except you carried me startin from calc 1.

[cannnonfoddder]

Need to cram for a maths exam? patrickJMT has got you covered ;)

[davoho]

Hey patrick I have one question: why do we randomly put "i j k" in the top row of this new determinant thing that we're calculating? In fact how did we know to construct this new determinant thing at all?

[singsango]

hey u seriouly a good teacher

[ruluhur]

You are awesome!!!!!

[AsakuraAvan]

i dont quite understand the right thumb rules....your thumb could really point into any direction you prefer.

[RooBars]

This has been great! I struggled through my graphics programming class, and managed to wind up in the top 15% but still didn't really understand this maths. It's now finals time, and with just a few short movies I completely get it. Thanks mate!

[noisygrass]

not as hard as I thought... however the placeholders i, j, k are a bit strange to me. you're taking the numbers at i, j, k just so out of the formula and that's it? does it have any background? are there more things that are calculated in a similar matter? I mean the placeholders. to me it looks like you were calculating some kind of complex numbers.

[RooBars]

@noisygrass to me it seems like an easy way to find the 2x2 matricies. for i, remove column i, j - remove column j, and k - remove column k and that is the 2x2 matrix for that letter. This doesn't seem necessary but it's a good way to show how things are related.

[iekenta03]

good shit man